Dynamic Strength - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 143

Function. Φ(σ). can. be. shown. as. the. Weibull. distribution. function,. see.
Equation.(5.71):

Φ(σ).=.1.-.P(t).. (5.71)

Here:.P(t).is.the.probability.of.collapse.in.the.local.part.of.the.construction.
from.compression.strength.
We.assume.that.the.general.strength.equals.unity.and.P(t).has.been.subor-
dinated.to.the.normal.distribution.law,.see.Equation.(5.72):

2 2 .

1 - t

(2p) 1/2

P(t) =

. (5.72)

where:
.parameter.t.is.equal.to:

= σ

-
Sj

σ

bi bm

. t . (5.73)

σ bi .is.a.current.strength.in.x,.y,.z.direction;
σ bm .is.a.middle.strength.in.x,.y,.z.direction;
Sj.is.a.sample.standard.deviation.for.each.environment,.see.Equation.(5.74):

n j

1

∑ σ

( )

2

2

. S = - σ . (5.74)

j bi bm

n - 1

J

I=1

Here:.n j .is.the.number.of.testing.samples.
Calculating.the.sample.mean.σ bm ,.see.Equation.(5.75):

n

i
= ∑

1

.. σ σ . (5.75)

bm bi

n

i

n=1

For.a.single.test.condition.(such.as.0°.compression.strength),.the.data.were.
collected.for.each.environment.being.tested..The.number.of.observations.in.
each. environmental. condition. was. n j . where. the. j. subscript. represents. the.
total.number.of.environments.being.pooled..If.the.assumption.of.normality.
was.signiicantly.violated,.the.other.statistical.model.should.be.investigated.
to.it.the.data..In.general,.the.Weibull.distribution.provides.the.most.conser-
vative.basic.value.
In.R..Talreja, 34 .the.Weibull.distribution.function.is.given.in.Equation.(5.76):